Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : In this paper we consider a new approach for single object segmentation in 3D images. Our model finds a surface that has two curves as boundary conditions and that minimizes the integral of a potential function that corresponds to the image features. These given curves are supposed to belong to the surface to extract and thus, constitute user given information. Our goal is achieved by building globally minimal paths between points located on each curve. To that end, we give some mathematical results on the equation satisfied by these paths and the link with the Eikonal equation. We then approximate the surface to extract by a discrete network of these paths. Furthermore, an interpolation method is used to build a mesh or an implicit representation based on the information retrieved from the network. Our paper describes a fast construction obtained by exploiting the Fast Marching algorithm and a fast analytical interpolation method. Moreover, a Level set method can be used to refine the segmentation when higher accuracy is required. The algorithm has been successfully applied to 3D medical images and synthetic images.
ARDON Roberto, COHEN Laurent
Université de PARIS - DAUPHINE
Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE
Téléphone : +33 (0)1 44-05-49-23 - fax : +33 (0)1 44-05-45-99